7. Wanda's Widgets used market surveys and linear regression to develop a demand function based on the wholesale price. The demand function is q = -140p + 9,000. The expense function is E = 2.00q + 16,000.
a. Express the expense function in terms of p.
b. At a price of $10.00, how many widgets are demanded?
c. How much does it cost to produce the number of widgets from part b?
I am so confused on how to answer these 3 sections, so if anyone could help I would really appreciate it!!
Answers
a. The expense function in terms of p is - 280p + 34, 000
b. At a price of $10.00, 7, 600 widgets are demanded
c. It costs $31, 200 to produce the number of widgets from part b
How to determine the valuesWe have that;
The demand function is q = -140p + 9,000The expense function is E = 2.00q + 16,000To express the expense function in terms of p, we have to take the following steps;
Substitute the value of q in the demand function into the function for the expense, we get;
Expense function = 2( -140p + 9,000) + 16, 000
Now, expand the bracket, we get;
Expense function = - 280p + 18, 000 + 16, 000
collect and add like terms
Expense function = - 280p + 34, 000
If p = $10. 00
Then,
Demand function is q = -140(10) + 9,000
expand the bracket
q = - 1400 + 9, 000
q = 7, 600
Substitute q in expense function
E = 2.00q + 16,000
E = 2. 00(7600) + 16, 000
E = $31, 200
Hence, the expense function is - 280p + 34, 000
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Related Questions
Use f(x) = 4x - 3 and g(x) = 5 - x2 to evaluate the expression.
(a)
(f o g)(x)
(b)
(g o f)(x)
A
Answers
The expression will be; part (a) (f o g)(-2) = 2 and part (b) (g o f)(-2) = -95
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given the functions as;
f(x)=4x-2
g(x)=5-x^2
We need to find (f o g)(-2)
So, first, we will find the function (f o g)(x) as follows:
[tex]\begin{gathered} \mleft(f\circ g\mright)(x)=f\lbrack g(x)\rbrack=4(5-x^2)-2 \\ (f\circ g)(x)=20-4x^2-2 \\ (f\circ g)(x)=18-4x^2 \end{gathered}[/tex]
Now, substitute with x = -2 then we get;
[tex](f\circ g)(-2)=18-4\cdot(-2)^2=18-4\cdot4=18-16=2[/tex]
Thus, the answer to the part is (a) (f o g)(-2) = 2
b) (g o f)(-2)
We need to find (g o f)(x) as follows:
[tex](g\circ f)(x)=g\lbrack f(x)\rbrack=5-(4x-2)^2[/tex]
Now Substitute with x = -2, then we get;
[tex]\begin{gathered} (g\circ f)(-2)=5-(4\cdot-2-2)^2 \\ =5-(-8-2)^2 \\ =5-(-10)^2 \\ =5-100 \\ =-95 \end{gathered}[/tex]
Thus, the answer to the part (b) is (g o f)(-2) = -95
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Seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary. Find the measures of these three angles.
Answers
The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.
How to find angles of a decagon?A decagon simony means a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.
Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.
Therefore,
1440 - 1220 = 220
Let the angles be a, b and c.
Therefore,
a + b + c =220
a + b = 90
b + c = 180
Hence,
a = 220 - 180
a = 40°
b = 90 - 40
b = 50°
c = 180 - 50
c = 130°
The angles are 40°, 50° and 130°.
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A telephone exchange operator assumes that 8% of the phone calls are wrong numbers.
If the operator is correct, what is the probability that the proportion of wrong numbers in a sample of 494 phone calls would differ from the population proportion by more than 3%? Round your answer to four decimal places.
Answers
The probability that the phone calls would differ from the population proportion by more than 3% is 0
How to determine the probability value?From the question, the given parameters about the distribution are
Proportion, p = 8%Sample size, n = 494The actual proportion, x = greater than 3%The mean is calculated as
Mean = np
So, we have
Mean = 8% * 494 = 39.52
The standard deviation is calculated as
Standard deviation = √np(1 - p)
So, we have
Standard deviation = √494 * 8% (1 - 8%) = 0.77
The z-score is calculated using the following formula
[tex]z = \frac{\bar p - p}{\sqrt{p(1 - p)}/n}[/tex]
Substitute the given parameters in the above equation
[tex]z = \frac{8\% - 3\%}{\sqrt{8\% * (1 - 8\%)}/494}[/tex]
Evaluate
z = 90.9
The probability is then calculated as:
P(x > 3%) = P(z > 90.9)
From the z table of probabilities, we have;
P(x > 3%) = 0
Hence, the probability is 0
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When driving mountain roads, road signs often indicate the steepness of the road as a % grade which represents the angle of elevation as the road rises. Imagine your job is to collect or measure the data that is needed to determine the % grade of mountain roads in a certain region of the U.S. Which of these quantities is needed for you to be able to use arcsine to calculate the % grade? Select all that apply.
a) The length of a section of the road
b) The angle of depression
c) The horizontal distance travelled
d) The change in elevation along a section of road
Answers
The quantity that is needed for you to be able to use arcsine to calculate the percentage grade is D. The change in elevation along a section of road
What is an elevation?A geographic location's elevation is its height above or below a set reference point, most typically a reference geoid, which is a mathematical model of the Earth's sea level as an equipotential gravitational surface.
Elevation is described as the height above the ground or other surface, as well as a location or position of elevation. A plane flying 36,000 feet above the ground is an illustration of elevation. A pope being elevated to the position of saint is an example of elevation.
When driving on mountain roads, road signs frequently reflect the route's steepness as a percentage grade, which represents the angle of elevation as the road increases. In this case, the correct option is D.
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Which of the following is the formula for the solutions of a quadratic equation ax2 + bx + c = 0?
Answers
bill wrote all the numbers from 1 to 1000. how many digits did he write down?
Answers
Answer:
2890 digits--------------------------
One - digit numbers1 to 9 ⇒ 9 numbersTwo - digit numbers10 to 99 ⇒ 100 - 10 = 90Three - digit numbers100 to 999 ⇒ 1000 - 100 = 900Four - digit number 1000 ⇒ 1Number of digits1*9 + 2*90 + 3*900 + 1 = 2890WILL GIVE BROANLYEST 80 POINTS!!!!!!! What is the volume of a rectangular prism with a length of twenty-two and one-half feet, a width of 12 feet, and a height of 13 feet?
7,800 ft3
3,510 ft3
1,755 ft3
five hundred sixty-two and one-half ft3
Answers
Answer:7,800
Step-by-step explanation:
Answer:
Option B (3,510ft) would be correct.
Step-by-step explanation:
The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases. It has 6 faces (all are rectangular),12 sides, and 8 vertices. As the rectangular prism is a three-dimensional shape (3D shape), the unit that is used to express the volume of the rectangular prism is cm3, m3 and so on. In mathematics, any polyhedron, having all such characteristics can be referred to as a Cuboid.
You owe $46,212.35 on a student loan that carries an APR of 6.9%. You place the loan into forbearance for 5 years. How much do you owe on the loan when it comes out of forbearance?
Answers
You owe on the loan is $64512.90
Given,
In the question:
You owe $46,212.35 on a student loan that carries an APR of 6.9%. You place the loan into forbearance for 5 years.
To find the how much do you owe on the loan when it comes out of forbearance?
Now, According to the question:
Based on the given conditions,
Formulate;
You owe $46,212.35 on a student
Interest is 6.9%
46212.35 x (6.9% +1)^5
Evaluate the equation/expression:
64512.90
Hence, You owe on the loan is $64512.90
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Gavin deposited money into his savings account that is compounded annually at an interest rate of 9% Gavin thought the equivalent quarterly interest rate would be 2.25% is Gavin correct?
Answers
The quarterly interest rate is equal to 2.25%. This implies that Gavin is correct.
How to determine the value of equivalent quarterly interest rate?Mathematically, the compound interest on an investment can be calculated by using this formula:A(t) = P(1 + r/n)^{nt}
Where:A represents the future value.
r represents the interest rate.
n represents the number of times compounded.
P represents the principal.
T represents the time measured in years.
In this scenario, Gavin's savings account is compounded annually at an interest rate of 9%. This ultimately implies that, the equivalent quarterly interest rate would be calculated by dividing the annual interest rate of 9% by 4 as follows:
Quarterly interest rate = 9/4
Quarterly interest rate = 2.25%
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Classify the polynomial by its degree: 4m³-9x² + 10
A) 0
B) 1st
C) 2nd
D) 3rd
E) 4th
Answers
What is the mean of these numbers? 53 29 47 36 65
Answers
Determine the next three terms in the following sequence:
-1, 1/2, -1/4, 1/8, __, __, __,….
A. 1/12, 1/24, 1/48
B. 1/16, 1/32, 1/64
C. -1/16, 1/32, -1/64
D. -1/12, 1/24, -1/48
Answers
The next three terms in the sequence are -1/16, 1/32, -1/64
The correct option is option C)
What is a sequence?
A sequence is an set of values separated by commas Referring to a generalized rule. They have a relation among them. One of the common sequences are arithmetic progression
We are given a sequence of -1, 1/2, -1/4, 1/8,
We have to describe the next three terms of the sequence
If we notice closely the given sequence is an geometric sequence
Hence they have a common factor known as common ratio
in it we divide a term by its previous term
Hence
Ratio= (1/2)/-1
Ratio = -1/2
Now to find the next terms we multiply this with the last term we get
1/8*-1/2= -1/16
Now Hence the next three terms are -1/16, 1/32, -1/64
The correct option is option c)
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Given CB || ED,;CB=ED prove CBF= EDF using isometric ridged transformation outline the necessary transformation to prove CBF = EDF using a paragraph proof. Be sure to name specific sides or angles used in the transformation and any congruency statements
Answers
The given triangle is rotated about 180 degrees and as such, we can say that the triangle CBF is congruent to the triangle EDF.
How to prove congruent angles?
From the attached image, we see that CB is parallel to ED. We also see that the transversal lines are BD and CE.
The point E will become the image of point C by a rotation of 180° around the point F.
Now, the point D will be the image of point B by a rotation of 180° around the point F.
Rotation is a type of transformation and as such ΔEDF will be the image of ΔCBF.
Therefore we can conclude that ΔCBF ≅ ΔEDF
The second way to prove this congruency is as follows;
∠B = ∠D (Due to the fact that alternate angles are congruent)
∠C = ∠E (Due to the fact that alternate angles are congruent)
Now, since CB ≅ ED , then it means that ΔCBF ≅ ΔEDF by SAS congruency postulate
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I can determine if a relation is a
function.
1. Use vertical line test to determine if
the graph is a function. Why or why not?
71
(
7
2
Z
2
4
Answers
Answer:
1st Graph : Function
2nd Graph : Not a Function
Step-by-step explanation:
For the 1st Graph , any Vertical Line will not pass the Graph in more than one Point , So it represents a Function
For the 2nd Graph , many Vertical Line will pass the Graph in two Points , So it is not a Function
rewrite 11/12 in two different ways
Answers
~
12 and another way is to do 12
~
11
Laura and Kirk are comparing how much they have been running. Laura has already
run 36 miles and Kirk has run 64. Laura begins running 21 miles per week and Kirk runs 17 miles
per week. How many additional weeks, w, will it take for their total distance run to be equal?
Answers
The additional weeks, w, will it take for their total distance run to be equal is 7 weeks.
How to calculate the number of weeks?From the information, Laura has already
run 36 miles and begins running 21 miles per week. This will be 36 + 21w.
Kirk has run 64 miles and runs 17 miles per week. This will be 64 + 17w
where w = number of weeks
This will be equated as:
36 + 21w = 64 + 17w
Collect like terms
21w - 17w = 64 - 36
4w = 28
Divide
w = 28/4
w = 7
It'll take 7 weeks.
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Find the value of x in the equation
4^x+16^x= 272
Answers
Answer:
x = 2
Step-by-step explanation:
Determine if the expression r - 5√r+r² is a polynomial or not. If it is a
polynomial, state the type and degree of the polynomial.
Answers
The expression r - 5√r+r² is a polynomial.
What is a polynomial?
Mathematical expressions called polynomials have one variable and many exponents.
The algebraic expression must have all of its exponents be non-negative integers in order for it to be a polynomial. As a general rule, an algebraic expression isn't a polynomial if it contains a radical.
No part of an algebraic expression should be - Variables' square roots. variable powers that are fractional. variable powers that are negative. variables in any fraction's denominator.
Exponents, variables, and constants make up a polynomial. The amount of terms a polynomial has determines its name.
Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.
The idea of the graph of a polynomial equation was first introduced by René Descartes in La géometrie, published in 1637.
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The expression r-5√r+r² is a polynomial. A polynomial is made up of variables, constants, and exponents.
Explain about the polynomial?Polynomials are mathematical expressions with one variable and several exponents.
The algebraic expression is a polynomial if and only if all of its exponents are non-negative integers. In general, if an algebraic expression contains a radical, it isn't a polynomial.
An algebraic expression should not contain any square roots of variables. fractional powers that are changeable. variable powers with negative powers. variables in the denominator of any fraction.
A polynomial is made up of variables, constants, and exponents. A polynomial's name is determined by the number of terms it contains.
There are numerous types of polynomials. respectively a monomial, a binomial, and a trinomial.
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100 POINTS!!!
2. Millicent's password for a website is a 5-digit number. The digits are the prime factors of 2,205 listed from least to greatest. What is Millicent's password?
33577
D 35577
B 33557
A 33357
Answers
Answer:
Step-by-step explanation:
I
-4x=76 x equals _-____________________________________________________________________________________________________________________________________________________________--
Answers
The value of x in the equation -4x = 76 is 19.
What is equation?The equals sign is used in equations to indicate the equality of two expressions in a formula.
Given:
-4x = 76,
-x = 76 / 4,
x = -19
Therefore, the value of x in the equation -4x = 76 is 19.
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one serving of a certain brand of yogurt contains 7g of fat. the low fat version contains 45.75% less fat per serving. how many grams of fat does one serving of the low fat yogurt contain?
Answers
The grams of fat that are contained in one serving of the low-fat yogurt are: 3.7968g.
How do we obtain the grams of fat for one serving of low-fat yogurt?To obtain the number of grams of fat that is contained in one serving of the low-fat yogurt, we need to first note the percentage content of the low-fat version of yogurt.
100 - 45.75% = 54.25% or 0.5425
Since one serving of the yogurt contains 7g of fat, then the low-fat serving will be equal to:
7g × 0.5425 = 3.7968
So, the total gram of fat for one serving of the low-fat yogurt is equal to:
3.7968g
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Hayley's fuel bills for her house increased from £76 a month in 2021
to £89 a month in 2022. Calculate the percentage increase in Hayley's
fuel bills from 2021 to 2022.
Give your answer correct to three significant figures.
Answers
The percentage increase in Hayley's fuel bills from 2021 to 2022 is equal to 17.105%.
What is a Percentage Increase?
The phrase "percentage increase" (or "percentage change" in general) refers to the difference between the final and starting values of a quantity, expressed as a percentage of that number's original value.
Steps to Calculate Percentage Increase?
The formula to calculate Increase (I) is given by, [tex]I=Y-X[/tex], where [tex]X[/tex] is the original value and [tex]Y[/tex] is the new value.The percentage increase formula is given by, [tex]\%I=\frac{I}{X} \times 100[/tex]Here, in the question, it is given that,
The original amount (X) or the fuel bill in 2021 is £76.
The new amount (Y) or the fuel bill in 2022 is £89.
So, the Increase (I) in the fuel bills from 2021 and 2022 is calculated as,
[tex]I=Y-X\\\implies I=89-76\\\implies I=13[/tex]
Now, we can calculate the percentage increase in fuel bills from 2021 to 2022 as,
[tex]\%I=\frac{I}{X} \times 100\\\implies \%I=\frac{13}{76} \times 100\\\implies \%I=17.105\%[/tex]
Therefore, the percentage increase in Hayley's fuel bills from 2021 to 2022 is 17.105%.
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please help me and please hurry. also please show working clearly!!
Answers
Answer:
The limit does not exist
Step-by-step explanation:
This is because the left hand limit is 3,we know this because as the graph approaches from the left side of the Cartesian plan the open dot is on 3
and the right hand limit is 1 because as the graph approaches the X=1 from the right hand side the open dot lands on 1
Since the left hand limit doesn't equal to right hand limit,the overall limit of x=1 doesn't exist.
Graph a linear function with the given slope and y-intercept slope:3 y-intercept: 10
Answers
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The linear function with a slope of 3 and y-intercept of 10 is y = 3x + 10.
\What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Slope = 3
y-intercept = 10
The equation of a line is given as y = mx + c
m = slope
c = y-intercept
Now,
m = 3
c = 10
So,
The linear function with a slope of 3 and y-intercept of 10 is y = 3x + 10.
Thus,
The linear function with a slope of 3 and y-intercept of 10 is y = 3x + 10.
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Find the value of x.
76
139
90°
X
63°
180°
41
90
Answers
The measure of the angle 'x' will be 41°. Then the correct option is c.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The measure of the angles will be 76° and 63°.
By the property Supplementary angle, the equation is given as,
76° + x + 63° = 180°
Simplify the equation, then we have
x + 139° = 180°
x = 180° - 139°
x = 41°
The measure of the angle 'x' will be 41°. Then the correct option is c.
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Find the formula, in standard form
y=ax2+bx+c , for a quadratic, that has roots at x=5+4√10 and x=5−4√10 , and has a leading coefficient of 1.
Answers
The quadratic equation in standard form that contains the roots 5 + 4√10 and 5 - 4√10 is y = x² - 10 · x - 135.
How to determine quadratic formula in standard form
In this question we must derive a quadratic equation in standard form, that is, a polynomial of the form:
y = a · x² + b · x + c
Where b / a = - r₁ - r₂ and c / a = r₁ · r₂ and r₁ and r₂ are the roots of the polynomial. If we know that a = 1, r₁ = 5 + 4√10 and r₂ = 5 - 4√10, then the quadratic equation is:
y = a · [x² + (b / a) · x + (c / a)]
y = x² + (- 5 - 4√10 - 5 + 4√10) · x + (5 + 4√10) · (5 - 4√10)
y = x² - 10 · x + 25 - 160
y = x² - 10 · x - 135
y = x² - 10 · x - 135 is the quadratic equation in standard form.
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Elizabeth and Herman are collecting aluminum cana for a frundraiser at their school. Elizabeth was able to collect 50 cans each day from Monday to Friday, Herman was able to collect double that amount each day except Friday, when he collected none. Each can is worth 2 cents. What are the quantities in this situation?
Answers
The total cans collected by both Elizabeth and Herman is 650 and the total amount of money realized is 1300 cents.
What is rate?A rate is a ratio in which the two terms being compared have different unit's.For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.
The aluminum cans collected by Elizabeth from Monday to Fridays is 50× 5days = 250 cans
Herman collected double from Monday to Thursday and collected non on Friday, therefore the total cans collected by Herman = 50×2× 4 days= 400cans
the total cans collected = 250+ 400 cans = 650cans
therefore the total money realized since 1 can is with 2 cent is 650× 2= 1300cents
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PLEASE HELP!!!! I WILL GIVE YOU BRAINLIST!! PLEASE ASAP :)
Which graph shows the image of ΔABC after a rotation about the origin?
Answers
Answer:
D.
Step-by-step explanation:
just click the rotate button until it matches one of the answers
Find the quotient.
2.4)7.68
Answers
Answer:0.3125
Step-by-step explanation:
none sry
y=2/3x-18 rate of change
Answers
The rate of change of the equation, y = 2/3x - 18, is: 2/3.
How to Determine the Rate of Change of a Linear Equation?The rate of change of a linear equation that is expressed in slope-intercept form as y = mx + b is represented by the value of m in the equation. It is also referred to as the slope of the equation.
For example, if we are given the equation, y = 4x + 5, the value of m is 4. This implies that the rate of change, which is the slope, is equal to 4.
In the same vein, we are given the equation, y = 2/3x - 18.
The value of m, which is the slope or rate of change in the equation y = 2/3x - 18 is equal to 2/3.
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